非光滑多目标区间优化的最优性条件

doi:10.6040/j.issn.1671-9352.0.2019.141

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (11): 26-34.doi: 10.6040/j.issn.1671-9352.0.2019.141

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非光滑多目标区间优化的最优性条件

钱鑫强,王开荣^*

重庆大学数学与统计学院, 重庆 401331

发布日期:2020-11-17
作者简介:钱鑫强(1995— ),男,硕士研究生,研究方向为最优化理论与算法. E-mail:xinqiang_qian@163.com*通信作者简介:王开荣(1964— ),男,博士,教授,研究方向为最优化理论与算法. E-mail:kairong@cqu.edu.cn
基金资助:
国家自然科学基金资助项目(11571055)

Optimality conditions on nonsmooth vector interval-valued optimization

QIAN Xin-qiang, WANG Kai-rong^*

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Published:2020-11-17

摘要/Abstract

摘要： 利用Clarke方向导数和Clarke次微分得到了非光滑多目标区间优化弱LU有效解的Fritz John最优必要条件。在广义不变凸性及函数正则性的假设下得到了KKT条件、充分性条件及相关对偶理论。利用了一些实例来验证理论的可行性,这些结论能够解决一般情形下多目标区间优化的相关问题。

关键词: 区间优化, 正则性, LU有效解, Mond-Weir对偶

Abstract: By using Clarke directional derivative and Clarke subdifferential, Fritz John optimal necessary conditions for weak LU efficient solutions of nonsmooth vector interval-valued optimization are obtained. Under the assumption of generalized invariant convexity and regularity of functions, KKT necessary optimality conditions, sufficient optimality conditions and related duality results are given. Some examples are used to verify the feasibility of the theory. These conclusions can solve the related problems of vector interval-valued optimization in general.

Key words: interval-valued optimization, regularity, LU efficient solution, Mond-Weir duality

中图分类号:

O221

钱鑫强,王开荣. 非光滑多目标区间优化的最优性条件[J]. 《山东大学学报(理学版)》, 2020, 55(11): 26-34.

QIAN Xin-qiang, WANG Kai-rong. Optimality conditions on nonsmooth vector interval-valued optimization[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(11): 26-34.

参考文献

[1] WU H C. The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function[J]. European Journal of Operational Research, 2007, 176(1):46-59.
[2] WU H C. Wolfe duality for interval-valued optimization[J]. Journal of Optimization Theory and Applications, 2008, 138(3):497-509.
[3] WU H C. The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions[J]. European Journal of Operational Research, 2009, 196(1):49-60.
[4] SUN Y H, WANG Laishen. Optimality conditions and duality in nondifferentiable interval-valued programming[J]. Journal of Industrial & Management Optimization, 2013, 9(1):131-142.
[5] ANTCZAK T. Optimality conditions and duality results for nonsmooth vector optimization problems with the multiple interval-valued objective function[J]. Acta Mathematica Scientia, 2017, 37(4):1133-1150.
[6] CHEN Xiuhong, LI Zhihua. On optimility conditions and duality for non-differentiable interval-valued programming problems with the generalized(F, ρ)convexity[J]. J Ind Mang Optim, 2018, 14(3):895-912.
[7] JAYSWAL A, AHMAD I, BANERJEE J. Nonsmooth interval-valued optimization and saddle-point optimality criteria[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2016, 39(4):1391-1411.
[8] CLARKE F H. Nonsmooth optimization[M]. New York: Wiley Interscience, 1983.

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非光滑多目标区间优化的最优性条件

Optimality conditions on nonsmooth vector interval-valued optimization

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